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Sliding mode control for discrete-time descriptor Markovian jump systems with two Markov chains

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Abstract

This paper investigates sliding mode control problems for discrete-time descriptor Markovian jump systems which are supposed to contain two mutually independent homogeneous Markov chains. Firstly, the stochastic admissibility of the system with two Markov chains is analyzed and several necessary and sufficient conditions are obtained. A mode-independent sliding surface is then constructed, the stability of sliding mode dynamics is analyzed and the sliding mode controller is synthesized to ensure the finite-time reachability of the predefined sliding surface. Since the sliding surface is mode-independent, the effects of the switchings between two sequential subsystems on the convergence of the sliding surface are avoided. Finally, a numerical example is presented to illustrate the effectiveness of the developed theoretical results.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grant 61273008 and 61673099, Science and Technology Research Fund of Liaoning Education Department under Grant L2013051, and Jiangsu Planned Projects for Postdoctoral Research Funds under Grant 1401044, respectively.

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Authors and Affiliations

  1. Institute of Systems Science, Northeastern University, Shenyang, 110819, China

    Qingling Zhang, Jinghao Li & Zhongyan Song

  2. State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, 110819, China

    Qingling Zhang & Jinghao Li

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  1. Qingling Zhang
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  2. Jinghao Li
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  3. Zhongyan Song
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Correspondence to Qingling Zhang.

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Zhang, Q., Li, J. & Song, Z. Sliding mode control for discrete-time descriptor Markovian jump systems with two Markov chains. Optim Lett 12, 1199–1213 (2018). https://doi.org/10.1007/s11590-016-1085-6

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  • DOI: https://doi.org/10.1007/s11590-016-1085-6

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